# Width

Width is the measure of an object from side to side.

## What is width

In geometry, the width is the shortest side of a rectangle. The longer side is typically referred to as the length. The term height rather than length is also commonly used alongside the width. This can lead to some confusion because all of these are measures of "length" while also using the term "length" to describe one of the sides. Generally, when length and width are used to describe the sides of a rectangle, the width is the shorter side and the length is the longer side, as shown in the figure below.

When width and height are used, the width is the measure from left to right while the height is the measure from top to bottom; note that this also assumes the rectangles are oriented such that their sides are horizontal and vertical, rather than at some angle. The door below is an example in which we are more likely to use width and height to describe the measurements of the door, rather than width and length.

## Length, width, and height

By convention, length, width, and height are typically used as follows:

• Width - the shortest side of the rectangle when used with length; side of the triangle that goes from left to right when used with height; sometimes used to describe the side that goes from left to right along with the length (in this case, it is possible for the width to be longer than the length).

• Length - the longest side of the rectangle. Ideally length should not be used in contexts where it would not be the longest side, though it is sometimes used this way.

• Height - the side measured from top to bottom regardless of relative size of the horizontal measure (it can be shorter than the width).

It is important to note that the above conventions are not definitive. There is no consensus on exactly how each term should be used, so they are largely used arbitrarily. The best way to avoid any confusion is to always label all figures being referenced.

It is also worth noting that the differences between these terms are largely a question of English rather than math. Consider the formula for the area of a rectangle, A = length × width. We could arguably use any of the terms, length, width, or height to describe the sides of the rectangle. Regardless what word we use, the formula remains the same. If we know the dimensions of the rectangle, we simply multiply the measure of the sides by each other to find the area.

### Difference between length and height

The difference between length and height when labeling rectangles is typically based on relative size or orientation:

• Use length if you want to differentiate sides of the rectangle based on relative size; the longer side is the length and the shorter side is the width.

• Use height if you want to differentiate the sides of the rectangle based on orientation; the vertical side is the height and the horizontal side is the width.

If using height, the following rectangles are labeled as follows:

If using length, the same rectangles are instead labeled as follows:

In the above examples, the rectangles are all oriented such that their sides are vertical and horizontal. In cases where they are oriented diagonally or in some other way, using length is clearer than using height.

## Length, width, height, and depth

In three dimensions, the difference between length, width and height are further complicated by the addition of terms such as depth and breadth. Given that the 3D object is level, they are generally used as follows:

• Width - the horizontal distance from side to side of the 3D object (often interchangeable with depth).

• Height - the vertical measure of the 3D object.

• Length - the longest dimension of the 3D object that is not the height.

• Depth (breadth) - the horizontal distance from the front to back of the 3D object (often interchangeable with width).

There is no consensus on how these terms are used, so other definitions may differ, but the above provides a general guideline. In 3D, labeling the object based on its orientation is typically clearer than doing so based on relative size. Although there is no consensus, length is arguably the most ambiguous of the above terms, so when it is possible to reference a figure without using length as one of the measures, it is advisable to do so. The following figure shows a few different ways to label a 3D object.

Notice how length, width, and depth are interchangeable to some degree. Given that the 3D object is level, as it is in the figure above, the only measurement we can reliably refer to without confusion is the height. If the figure is oriented diagonally or in some other manner, what we mean by height may not be immediately clear. For this reason, when it comes to the terms we use, the ones we choose do not really matter. As a reader, we cannot reliably know to which side someone is referring without labels on the figure. We can only guess based on convention and what we have been taught.

### Depth vs width

By convention, the depth of a 3D object is its measure from front to back. The width is the measure of the object from side to side. However, this is just convention, and labeling often happens arbitrarily. Consider the following figure:

In this figure, the definitions of width and height, detailed above, apply; the width is the measure from side to side and the depth is the measure from front to back. However, if we were told that this same figure is a pool, it would make more sense to label it as follows:

This demonstrates how arbitrary these measures really are, so as long as we are consistent and clear with our labeling, the choice of words we use for the dimensions of a rectangle is not particularly important from a mathematical perspective.